For the sake of simplicity, the above discussions on channel estimation schemes take the narrow band as an example. The similar idea can be extended to the wideband orthogonal frequency division multiplexing (OFDM) channel estimation. Specifically, the channel on each sub-carrier can be estimated separately as in a narrow band system, such as [1]}. It is noted that the reflecting vector \(\mathbf {\theta }\)  at the RIS are the same for all sub-carriers. Besides, by considering the common sparsity of angular domain channels among different sub-carriers, [2]} proposed a joint overhead-reduced channel estimation scheme for all sub-carriers, where a denoising convolution neural network (DnCNN) is used to improve the estimation accuracy.
